Enter the coordinates of the vertex of the graph of y = 2(x + 5)2 − 4.
Vertex: (
,
)
Answers
9514 1404 393
Answer:
(-5, -4)
Step-by-step explanation:
Compare the given equation to vertex form:
y = a(x -h)² +k
You see that a=2, h=-5, k=-4.
The vertex is (h, k) = (-5, -4).
Related Questions
Find the solution of the differential equation f' (t) = t^4+91-3/t
having the boundary condition f(1) =1/4
Answers
Answer:
[tex]\displaystyle f(t) = \frac{t^5}{5} + 91t - 3ln|t| - \frac{1819}{20}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to RightEquality Properties
Multiplication Property of EqualityDivision Property of EqualityAddition Property of EqualitySubtraction Property of EqualityAlgebra I
FunctionsFunction NotationCalculus
Derivatives
Derivative Notation
Antiderivatives - Integrals
Integration Constant C
Integration Rule [Reverse Power Rule]: [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]
Integration Property [Addition/Subtraction]: [tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]
Integration Property [Multiplied Constant]: [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle f'(t) = t^4 + 91 - \frac{3}{t}[/tex]
[tex]\displaystyle f(1) = \frac{1}{4}[/tex]
Step 2: Integration
Integrate the derivative to find function.
[Derivative] Integrate: [tex]\displaystyle \int {f'(t)} \, dt = \int {t^4 + 91 - \frac{3}{t}} \, dt[/tex]Simplify: [tex]\displaystyle f(t) = \int {t^4 + 91 - \frac{3}{t}} \, dt[/tex]Rewrite [Integration Property - Addition/Subtraction]: [tex]\displaystyle f(t) = \int {t^4} \, dt + \int {91} \, dt - \int {\frac{3}{t}} \, dt[/tex][1st Integral] Integrate [Integral Rule - Reverse Power Rule]: [tex]\displaystyle f(t) = \frac{t^5}{5} + \int {91} \, dt - \int {\frac{3}{t}} \, dt[/tex][2nd Integral] Integrate [Integral Rule - Reverse Power Rule]: [tex]\displaystyle f(t) = \frac{t^5}{5} + 91t - \int {\frac{3}{t}} \, dt[/tex][3rd Integral] Rewrite [Integral Property - Multiplied Constant]: [tex]\displaystyle f(t) = \frac{t^5}{5} + 91t - 3\int {\frac{1}{t}} \, dt[/tex][3rd Integral] Integrate: [tex]\displaystyle f(t) = \frac{t^5}{5} + 91t - 3ln|t| + C[/tex]Our general solution is [tex]\displaystyle f(t) = \frac{t^5}{5} + 91t - 3ln|t| + C[/tex].
Step 3: Find Particular Solution
Find Integration Constant C for function using given condition.
Substitute in condition [Function]: [tex]\displaystyle f(1) = \frac{1^5}{5} + 91(1) - 3ln|1| + C[/tex]Substitute in function value: [tex]\displaystyle \frac{1}{4} = \frac{1^5}{5} + 91(1) - 3ln|1| + C[/tex]Evaluate exponents: [tex]\displaystyle \frac{1}{4} = \frac{1}{5} + 91(1) - 3ln|1| + C[/tex]Evaluate natural log: [tex]\displaystyle \frac{1}{4} = \frac{1}{5} + 91(1) - 3(0) + C[/tex]Multiply: [tex]\displaystyle \frac{1}{4} = \frac{1}{5} + 91 - 0 + C[/tex]Add: [tex]\displaystyle \frac{1}{4} = \frac{456}{5} - 0 + C[/tex]Simplify: [tex]\displaystyle \frac{1}{4} = \frac{456}{5} + C[/tex][Subtraction Property of Equality] Isolate C: [tex]\displaystyle -\frac{1819}{20} = C[/tex]Rewrite: [tex]\displaystyle C = -\frac{1819}{20}[/tex]Substitute in C [Function]: [tex]\displaystyle f(t) = \frac{t^5}{5} + 91t - 3ln|t| - \frac{1819}{20}[/tex]∴ Our particular solution to the differential equation is [tex]\displaystyle f(t) = \frac{t^5}{5} + 91t - 3ln|t| - \frac{1819}{20}[/tex].
Topic: AP Calculus AB/BC (Calculus I/II)
Unit: Integration
Book: College Calculus 10e
jack bought a mother bike the original price was 1300 but he got a discount of 20% what was the discounted price of the bike
Answers
Which is the volume of a sphere with diameter
50 cm?
Answers
Answer:
V =65416.666666 cm^3
Step-by-step explanation:
The volume of a sphere is given by
V = 4/3 pi r^3
The diameter is 50 so the radius is 1/2 of the diameter
r = 1/2 (50) = 25
V = 4/3 ( pi) (25)^3
V = 4/3 (pi) 15625
V =20833.3333 pi
Using 3.14 for pi
V =65416.666666 cm^3
Answer:
V =65416.666666 cm^3
Step-by-step explanation:
The volume of a sphere is given by
V = 4/3 pi r^3
The diameter is 50 so the radius is 1/2 of the diameter
r = 1/2 (50) = 25
V = 4/3 ( pi) (25)^3
V = 4/3 (pi) 15625
V =20833.3333 pi
Using 3.14 for pi
V =65416.666666 cm^3
HELPPPP PLZZZZZzz HELLP FAST I NEED TO PASS
Answers
Answer:
✬ m∠Q= 105°➬➬➬➬➬➬➬➬
[tex]6x+5+(11x-5)+x=180^o[/tex]
[tex]18x=180[/tex]
[tex]x=10[/tex]
☄m∠Q=105°
❆❆❆❆❆❆❆❆❆❆❆❆
hope it helps....
have a great day!!
Can someone help me pls pls help with this question
Answers
Answer:
D.
Step-by-step explanation:
The mean is 11,000
Last week at the business where you work , you sold 120 items. The business paid $1 per item and sold them for $3 each. What profit did the business make from selling the 120 items
Answers
Answer:
240
Step-by-step explanation:
They spent $120 buying 120 items, so they have -$120. By selling the items at 3x the price, they gained the 120 back and made a profit of 240 (120 x 2).
3-1=2
120 x 2=240
Which is the inverse of the following statement?
If the measure of an angle is 90°, then it is a right angle.
Answers
The track team has 12 more boys than girls. There are a total of 142 team members. How many boys and girls are on the team?
Answers
Answer:
77 boys, 65 girls
Step-by-step explanation:
x as the variable to represent amount of girls, and there are 12 more boys than girls (x+12). So the equation would be:
x + x + 12 = 142
2x + 12 = 142
x = 65
65 girls
then 65+ 12 = 77 boys
The value of the 2 in 43,290 is
times the value
of the 2 in 32,865.
Answers
9514 1404 393
Answer:
1/10
Step-by-step explanation:
The value of any digit is found by setting all other digits to zero.
The value of the 2 in 43,290 is 200.
The value of the 2 in 32,865 is 2,000.
200 is 200/2000 = 1/10 times 2000
The value of 2 in 43,290 is 1/10 times the value of 2 in 32865.
Pedro solves the quadratic equation x^2+6x –14 using the quadratic formula. In which step did Pedro make an error?
Answers
9514 1404 393
Answer:
correct choice is marked
Step-by-step explanation:
The error is in step 2. The square root cannot be distributed to a sum.
I need help with this three problems (with procedure)
Answers
Answer:
13. [tex]x^{3} y^3[/tex] cubic units
14. 43 million; 79 million; 3.6 × [tex]10^7[/tex]
15. 2.68 × [tex]10^5[/tex]
Step-by-step explanation:
Suppose you are investigating the relationship between two variables, traffic flow and expected lead content, where traffic flow is a predictor of lead content. You find the 95% CI for expected lead content when traffic flow is 15, based on a sample of n= 10 observations, is (461.7, 598.1).
Required:
What parameter is this interval estimating?
Answers
Answer:
The answers is " Option B".
Step-by-step explanation:
[tex]CI=\hat{Y}\pm t_{Critical}\times S_{e}[/tex]
Where,
[tex]\hat{Y}=[/tex] predicted value of lead content when traffic flow is 15.
[tex]\to df=n-1=8-1=7[/tex]
[tex]95\% \ CI\ is\ (463.5, 596.3) \\\\\hat{Y}=\frac{(463.5+596.3)}{2}\\\\[/tex]
[tex]=\frac{1059.8}{2}\\\\=529.9[/tex]
Calculating thet-critical value[tex]t_{ \{\frac{\alpha}{2},\ df \}}=-2.365[/tex]
The lower predicted value [tex]=529.9-2.365(Se)[/tex]
[tex]463.5=529.9-2.365(Se)\\\\529.9-463.5=2.365(Se)\\\\66.4=2.365(Se)\\\\Se=\frac{66.4}{2.365} \\\\Se=28.076[/tex]
When [tex]99\%[/tex] of CI use as the expected lead content: [tex]\to 529.9\pm t_{0.005,7}\times 28.076 \\\\=(529.9 \pm 3.499 \times 28.076)\\\\=(529.9 \pm 98.238)\\\\=(529.9-98.238, 529.9+98.238)\\\\=(431.662, 628.138)\\\\=(431.6, 628.1)[/tex]
What is 8.75% of 172?
Answers
Answer:
15.05 is your answer.
Step-by-step explanation:
To find our answer we will first divide 8.75 by 100 since it is a percentage. 8.75 ÷ 100 = 0.0875
Now we will take 0.0875 and multiply it by 172 and we get 15.05. Therefore, 15.05 is our answer
Hey there!
8.75% of 172
The word “of” means multiply in mathematical terms.
8.75% * 172
8.75% = 8.75/100 = 0.0875
0.0875 * 172
= 301/20
= 15.05
Answer: 301/20 OR 15.05
(BOTH ANSWERS WORK because they are both equivalent)
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
Find the area of this triangle. Round to the nearest tenth.
Answers
Area = 1/2 × 24 × 11 × Sin(76)
Area = 12 × 11 × 0.9703
Area = 132 × 0.9703
Area = 128.0796
Area = 128.1 in^2
Find the value of x.
Answers
The hypotenuse function is correct, but the main function has a problem. Explain why it may not work, and show a way to fix it. Your fix must be to the main function only; you must not change the hypotenuse function in any way.
Answers
Answer: hello your question is incomplete attached below is the missing codes
Answer : It may not work because; the double pointer P was not allotted a double using a new double ( I.e. Error in the main function ) also the cout statement was not written in the main function
Step-by-step explanation:
It may not work because; the double pointer P was not allotted a double using a new double ( I.e. Error in the main function ) also the cout statement should be moved to the Main
The correction is below
{
double* p = new double;
hypotenuse(1.5, 2.0, p);
cout << "The hypotenuse is " << *p << endl;
}
find the largest prime factor of 6108
Answers
Answer:
509
Step-by-step explanation:
There are 4 prime factors of 6108
6108 ÷ 2 = 3054
3054 ÷ 2 = 1527
1527 ÷ 3 = 509
509 ÷ 509 = 1
Exponential Growth/Decay
Plz help!!!
Answers
Answer:
a) 82.
b) So a growth factor of 0.025
c) 2.5%.
d) f(5) = 93, which means that the population of the island on January 1st 2026 is of 93.
Step-by-step explanation:
Exponential equation of population growth:
The exponential equation for population growth has the following format:
[tex]f(x) = x(0)(1+r)^x[/tex]
In which x(0) is the initial value and r is the growth factor, as a decimal.
In this question:
In x years after 2021:
[tex]f(x) = 82(1.025)^x[/tex]
a)
This is f(0). So
[tex]f(0) = 82(1.025)^0 = 82[/tex]
So 82.
b)
We have to find r. So
[tex]1 + r = 1.025[/tex]
[tex]r = 1.025 - 1 = 0.025[/tex]
So a growth factor of 0.025.
c)
Growth factor multiplied by 100%.
So 0.025*100% = 2.5%.
d)
f(5) = population in 5 years after January 1st 2021, that is, January 1st 2026.
[tex]f(5) = 82(1.025)^5 = 93[/tex]
f(5) = 93, which means that the population of the island on January 1st 2026 is of 93.
GIVING OUT BRAINLIEST PLS HELP! ALMOST DUE
Answers
Answer:
I think it's option B
What combination of transformations is shown below?
Answers
Explanation:
To go from figure 1, to figure 2, we apply a translation (aka "shifting"). Specifically, we translate 3 units to the right and 4 units up.
To go from figure 2 to figure 3, we apply a reflection. The mirror line is vertical and it is along the shared segment of figures 2 and 3.
What is the outlier for the data set?
19, 19, 27, 21, 77, 18, 23, 29
Answers
Answer: 77
Step-by-step explanation:
c and d for 20 pts
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Answers
Answer:
C. a = 7
D. c = -3
Step-by-step explanation:
C. 7(2a + 3) + 21 = 100+ 40
14a + 21 + 21 = 140
14a = 140 - 21 - 21
14a = 98
a = 7
D. 6+ 14 - 12c = 56
20 - 12c = 56
-12c = 56 - 20
-12c = 36
c = - 3
Answer:
Step-by-step explanation:
c.7(2a+3)+21=100+40
14a+21+21=140
14a+42=140
14a=140-42
a=98/14
a=7
d.6+14-12c=56
20-12c=56
-12c=56-20
c=36/-12
c=-3
Plz help me!!(ᗒᗣᗕ)՞
Plz!
Answers
Answer:
A) 64 cm²
Step-by-step explanation:
Trapezoid area formula:
[tex]A=\frac{a+b}{2} h[/tex]
Given:
a = 6
b = 10
h = 8
Work:
[tex]A=\frac{a+b}{2} h\\\\A=\frac{6+10}{2} *8\\\\A=\frac{16}{2} *8\\\\A=8*8\\A=64[/tex]
4d = -16
what’s the value of d
Answers
[tex]4d = - 16 \\ \\ d = \cancel \frac{ - 16}{4} \\ \\ d = - 4[/tex]
Hope This Helps YouAnswer:
The value of d is -4. When you multiply 4 by -4 you get -16. If you want me to elaborate, let me know.
Step-by-step explanation:
Help will be appreciated
Answers
Answer:
48
hope this helps
have a good day :)
Step-by-step explanation:
Answer:
48
the picture 20 words or longer for the answer so this is extra text
Choose the best estimate for the multiplication problem below. 56 x 51
A. 2000
B. 3000
C. 4100
Answers
Answer:
B
Step-by-step explanation:
Explanation: 56 multiply 51 is 2856 and 3000 is the closest to 2856.
Also pls mark me as brianliest!!
plsss help!! is this a right triangle if no or yes please explain why??
Answers
Answer:
yes, it is a right triangle
Step-by-step explanation:
the other two angles are 35 and 55 degrees
Answer:
is NOT a right triangle
Step-by-step explanation:
is a right triangle if it checks the Pythagorean Th.
12² = 10² + 7²
144 = 100+49
144 = 149 False
The cost of producing x units of a product is $1.25 per unit plus $1,000 in flat production costs. If you spend $3,000 on production costs, how many units were produced?
3,000=1.25x+1,000
Answers
Answer:
1600
Step-by-step explanation:
1.25x + 1000 = 3000
Subtract 1000 from both sides
1.25x = 2000
Divide both sides by 1.25
x = 1600
The product of b and 3
Answers
Answer and Step-by-step explanation:
The product of a two numbers/values is the result of multiplying two numbers/values.
So, multiply b and 3 together.
3b is the answer.
#teamtrees #PAW (Plant And Water)
Determine the missing angle in the picture below.
Answers
Answer:
x =41.18114952
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
We know the hypotenuse and adjacent sides
cos theta = adjacent / hypotenuse
cos x = 14.3/19
taking the inverse cos of each side
cos^-1 (cos x) = cos ^-1 ( 14.3/19)
x =41.18114952
Answer:
Step-by-step explanation:
take x degree as reference angle
using cos rule
cos x=adjacent/hypotenuse
cos x=14.3/19
cos x=0.75
x=cos 41
x= 41 degree